All calculatorsKinetic Energy Calculator
Calculate kinetic energy from mass and speed: KE = ½mv². Solve for KE, solve for speed, or explore rolling motion (translational + rotational). Includes steps, quick picks, a mini energy bar, and a fun “equivalent drop height” badge.
Background
Kinetic energy measures energy of motion. For straight-line motion, KE = ½mv² (so speed matters a lot because it’s squared). For rolling objects, energy is split between translation and rotation: KE = ½mv² + ½Iω².
How to use this calculator
- Pick a mode: m + v → KE, KE + m → v, or rolling.
- Choose units (kg/g, m/s, km/h, mph).
- Click Calculate to get results, visuals, and the equivalent “drop height” badge.
How this calculator works
- Linear motion: KE = ½mv²
- Solve for speed: v = √(2KE/m)
- Rolling: KE = ½mv² + ½Iω² with v=ωR
- Equivalent drop: h = KE/(mg)
Formula & Equation Used
Kinetic energy: KE = ½mv²
Speed from energy: v = √(2KE/m)
Rolling energy: KE = ½mv² + ½Iω²
Equivalent drop height: h = KE/(mg)
Example Problems & Step-by-Step Solutions
Example 1 — KE from mass + speed
- A 0.145 kg baseball moves at 40 m/s. Find KE.
- Use KE = ½mv².
- KE = 0.5 × 0.145 × 40² = 116 J (about).
Example 2 — Speed from energy
- A 2 kg object has 5 kJ of kinetic energy. Find v.
- v = √(2KE/m)
- v = √(2×5000 / 2) = √5000 ≈ 70.7 m/s
Example 3 — Rolling energy split
- A 2 kg solid sphere rolls at 8 m/s. Find total KE.
- Solid sphere factor makes KE = (½mv²)·(1 + 2/5) = (½mv²)·1.4.
- Translational: ½·2·8² = 64 J. Total: 64·1.4 = 89.6 J.
Frequently Asked Questions
Q: Why does speed matter so much?
Because v is squared. Doubling speed quadruples kinetic energy.
Q: What does “equivalent drop height” mean?
It’s the height that would give the same energy from gravity: mgh = KE.
Q: Why is rolling KE bigger than ½mv²?
Because some energy goes into rotation, not just translation.
